Problems in Real Analysis : Advanced Calculus on the Real Axis / by Teodora-Liliana Radulescu, Vicentiu D. Radulescu, Titu Andreescu.

Springer eBooks

Sequences, Series, and Limits -- Sequences -- Series -- Limits of Functions -- Qualitative Properties of Continuous and Differentiable Functions -- Continuity -- Differentiability -- Applications to Convex Functions and Optimization -- Convex Functions -- Inequalities and Extremum Problems -- Antiderivatives, Riemann Integrability, and Applications -- Antiderivatives -- Riemann Integrability -- Applications of the Integral Calculus -- Basic Elements of Set Theory.

Problems in Real Analysis: Advanced Calculus on the Real Axis features a comprehensive collection of challenging problems in mathematical analysis that aim to promote creative, non-standard techniques for solving problems. This self-contained text offers a host of new mathematical tools and strategies which develop a connection between analysis and other mathematical disciplines, such as physics and engineering. A broad view of mathematics is presented throughout; the text is excellent for the classroom or self-study. It is intended for undergraduate and graduate students in mathematics, as well as for researchers engaged in the interplay between applied analysis, mathematical physics, and numerical analysis. Key features: *Uses competition-inspired problems as a platform for training typical inventive skills; *Develops basic valuable techniques for solving problems in mathematical analysis on the real axis and provides solid preparation for deeper study of real analysis; *Includes numerous examples and interesting, valuable historical accounts of ideas and methods in analysis; *Offers a systematic path to organizing a natural transition that bridges elementary problem-solving activity to independent exploration of new results and properties.

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